Unique continuation for solutions to PDE’s; between Hörmander’s theorem and Holmgren’s theorem. (English) Zbl 0846.35021

The author proves a new unique continuation result for solutions of a certain class of partial differential equations under some partial analyticity assumptions on the coefficients. Their result is weaker than Holmgren’s Theorem (which applies to analytic coefficients) but stronger than Hörmander’s Theorem (which applies to \(C^1\) coefficients). Some applications to the wave and the Schrödinger equation are presented. In particular, he obtains a conjecture by Hörmander on the wave equation.
Reviewer: J.I.Diaz (Madrid)


35B60 Continuation and prolongation of solutions to PDEs
35A07 Local existence and uniqueness theorems (PDE) (MSC2000)
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